Time-domain aeroservoelastic modeling using weighted unsteady aerodynamic forces

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A modeling method for constructing a state-space aeroservoelastic mathematical model for time-domain analysis with a low number of aerodynamic lag states is presented. The modeling method employs the minimumstate method for rational approximation of tabulated unsteady aerodynamic force coefficients at various reduced-frequency values. The approximation method is modified to deal with weighted aerodynamic data and with alternative constraint combinations. Two weighting types are analyzed and discussed. The first weighting is normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced-frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms at the expense of less important ones. The analytical developments are presented and numerical examples, which demonstrate various features of this method, are shown to yield significant reduction in model size per given accuracy relative to other rational approximation methods.